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Efficient inference in state-space models through adaptive learning in online Monte Carlo expectation maximization

Author

Listed:
  • Donna Henderson

    (University of Oxford)

  • Gerton Lunter

    (Unversity of Oxford)

Abstract

Expectation maximization (EM) is a technique for estimating maximum-likelihood parameters of a latent variable model given observed data by alternating between taking expectations of sufficient statistics, and maximizing the expected log likelihood. For situations where sufficient statistics are intractable, stochastic approximation EM (SAEM) is often used, which uses Monte Carlo techniques to approximate the expected log likelihood. Two common implementations of SAEM, Batch EM (BEM) and online EM (OEM), are parameterized by a “learning rate”, and their efficiency depend strongly on this parameter. We propose an extension to the OEM algorithm, termed Introspective Online Expectation Maximization (IOEM), which removes the need for specifying this parameter by adapting the learning rate to trends in the parameter updates. We show that our algorithm matches the efficiency of the optimal BEM and OEM algorithms in multiple models, and that the efficiency of IOEM can exceed that of BEM/OEM methods with optimal learning rates when the model has many parameters. Finally we use IOEM to fit two models to a financial time series. A Python implementation is available at https://github.com/luntergroup/IOEM.git .

Suggested Citation

  • Donna Henderson & Gerton Lunter, 2020. "Efficient inference in state-space models through adaptive learning in online Monte Carlo expectation maximization," Computational Statistics, Springer, vol. 35(3), pages 1319-1344, September.
    • Handle: RePEc:spr:compst:v:35:y:2020:i:3:d:10.1007_s00180-019-00937-4
    DOI: 10.1007/s00180-019-00937-4
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    References listed on IDEAS

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    1. Ravi Varadhan & Christophe Roland, 2008. "Simple and Globally Convergent Methods for Accelerating the Convergence of Any EM Algorithm," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(2), pages 335-353, June.
    2. R. H. Shumway & D. S. Stoffer, 1982. "An Approach To Time Series Smoothing And Forecasting Using The Em Algorithm," Journal of Time Series Analysis, Wiley Blackwell, vol. 3(4), pages 253-264, July.
    3. Fearnhead, Paul & Vasileiou, Despina, 2009. "Bayesian Analysis of Isochores," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 132-141.
    4. Cornett, Marcia Millon & Schwarz, Thomas V. & Szakmary, Andrew C., 1995. "Seasonalities and intraday return patterns in the foreign currency futures market," Journal of Banking & Finance, Elsevier, vol. 19(5), pages 843-869, August.
    5. repec:wyi:journl:002173 is not listed on IDEAS
    6. Olivier Cappé & Eric Moulines, 2009. "On‐line expectation–maximization algorithm for latent data models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 593-613, June.
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